Question

how to examine continuity from graph?
explain with an example.​

Answer 1

Answer:

In calculus, a function is continuous at x = a if - and only if - all three of the following conditions are met:

The function is defined at x = a; that is, f(a) equals a real number.

The limit of the function as x approaches a exists.

The limit of the function as x approaches a is equal to the function value at x = a.

Is f(x) continuous at x = 0?

Graph of y=f(x) near x=0

To check for continuity at x = 0, we check the three conditions:

Is the function defined at x = 0? Yes, f(0) = 2

Does the limit of the function as x approaches 0 exist? Yes

Does the limit of the function as x approaches 0 equal the function value at x = 0? Yes

Since all three conditions are met, f(x) is continuous at x = 0.